Linking transformation but not other data (ex. Modifiers) in two objects
For arrays from object offset, parent the object to the array.  Empties cannot have modifiers of any kind, so I'm not sure what you're talking about with it acquiring the array.  This is likely a misinterpretation of something, but if it's not, then it's a bizarre bug.  A video of the problem, or a file with explicit instructions to recreate, would be necessary to answer in more detail.

Selecting the empty will not select the barrel.  Regardless of selection in viewport or outliner.  I wish there was an interface to make Blender behave like you describe, it would be useful for a few specialist things.  Again, I suspect you're misinterpreting something, and video or file+instruction would be necessary to give more detail.

To answer the explicit question, for perfect linking of transformation data, use object constraints.  &quot;Copy transforms&quot; copies all data.  You also have &quot;copy position&quot;, &quot;copy rotation&quot;, &quot;copy scale&quot;, all pretty self explanatory.  Generally, you'd be using these world-&gt;world space, but there are times that you could parent an object to an empty and use local space coordinates to achieve other effects.  (However, again, I strongly suspect that there's some misinterpretation of what Blender's doing here, and even though it answers your explicit question, I doubt that it will do what you expect it to.)